I couldn't fathom keeping a cocker spaniel or sussex spaniel outside. Those are not outside dogs. I don't know what being Nevada has to do with anything. Dogs thrive on attention and they want to be around people, they'd be miserable outside. But you have some options.
First of all your dad said they could stay in your bedroom, so worst case scenario, do that. Take em outside for walks and play time so they don't get bored, but they'll probably be happier to be staying in your room, even if it's small, than being alone outside.
But first you could try reasoning with your dad. Tell him how you're prepared to deal with the shedding. Those kind of spaniels need constant grooming anyway, so agree to brush out their coats daily. Do your dogs shed a lot? You could get a shedding brush and use that outside. But mostly just normally daily brushing will help with the shedding. If you live where it's hot and humid you can keep their coats shaved. Agreeing to sweep the floor daily is a good thing too. Do you parents see you as reliable with chores like that, or do they think it's an empty promise? If so you might need to take on some consequences. For example, "and if I don't sweep the floors every day after school then I don't get any allowance." Secondly, get a lot of information together. Pull information from websites such as http://www.unchainyourdog.org/
. Dad's are often persuaded by financial statements. Cocker Spaniels are susceptible to skin conditions when left outdoor for days on end, especially if weather conditions are severe, too much sun. If it's hot and humid, especially in the summer, dogs are prone to heat strokes and dehydration. As you mentioned small dogs like yours that are left outside are open to attacks from predators that could leave some costly wounds. If you forget to give heartworm preventative for only one month, having them outside means they have great exposure to that disease, among others. Call a vet and get the costs to treat some of these conditions and spell it all out for your dad. Is he willing to spend $1500 on heartworm treatment because he's leaving his dogs outside 24/7, etc. Get all your information together, print it out or hand write it so that it looks nice and present it to your parents during dinner. If you have other family members try and get them on your side beforehand.
If this was me and my dad wouldn't listen to reason, then as a last resort I would protest, of sorts, by pithcing a tent and sleeping outside with the dogs day in and day out. If it's safe enough for the dogs, then it's safe enough for me, right.
I can understand not wanting to have a new house that you just built yourself getting messed up. But kicking the dogs outside is not an acceptable solution. Tell him you understand his concerns. But provide some alternative solutions, brushing their hair, sweeping daily, etc. And good luck.